If I read the manuals correctly, the "controller" module for those fans that comes with the case only controls their colours. It seems (not sure!) that their speeds are controlled by the mobo fan header you connect to the fan "controller". You are supposed to connect a cable from one mobo SYS_FAN header to the controller's 3-pin input connector for this.
Now, the fans and the supplied controller are designed for use with 3-pin fan systems - that is, a SYS_FAN header that uses Voltage Control Mode. Well, your mobo does exactly that, so you're good there.
Regarding the number of fans, don't worry. Any standard fan header can supply up to 1.0 amps total to all its fans, and most common case ventilation fans (yours included) use no more than 0.2 amps each. So 3 fans on one mobo SYS_FAN header is entirely OK.
I doubt you need a splitter. If I understand the manuals correctly, you will plug all your fans into that included controller so it can control their colours. BUT it also takes the power from ONE SYS_FAN header and distributes it to all three fans, just as a Splitter would do. Since your mobo SYS_FAN header will use varying voltage to control whatever is connected to it, all three fans will have their speeds controlled identically by that mobo header. Now, IF the case also has fan speed selection buttons on it associated with the fan "controller", I suggest you start by setting it to High (so it does not interfere) and then see if the mobo actually does change the fan speeds as your workload changes.